Question

Every year on April 1, Anytown Tigers and Someville Lions play a soccer game. It is always a high-scoring game; the number of goals scored follows a Poisson
process with the average rate of one goal per 5 minutes. ( A soccer game consists of two halves, 45 minutes each. )

a) What is the probability that the fourth goal is scored during the last 10 minutes of
the first half?
b) What is the probability that the fifth goal is scored during the last 15 minutes of
the first half?
c) Find the probability that more than 20 goals are scored during the game. (Use Normal approximation.) Every year on A

Answer 1

oh, i can do this but i will need to dig in old textbooks a bit.

Answer 2

ok, i think i got a solution to a)

Answer 3

Actually i noticed a flaw in my logic hold on, it's a toughy.

Answer 4

alright. it takes a while to write down but i guess i got it for real this time

Answer 5

so, since the 4th goal has to be scored in the last 10 minutes of the first half, 35 minutes must have had passed with 3 or less goals. while we would expect 7 goals in the first 35 minutes.

Answer 6

now that alone would not give us a solution, because not only must we have the first 35 minutes go with 3 or less goals, we ALSO need a 4th goal in the next 10 minutes.

Answer 7

so you either have 3 goals in the first 35 AND 1 (or more) goals in the next 10 minutes, OR 2 goals in the first 35 minutes AND 2 (or more) goals in the next 10 minutes OR 1 goal in the first 35 minutes AND 3 (or more) goals in the next 10 minutes OR 0 goals in the first 35 minutes AND at least 4 goals in the next 10 minutes.

Answer 8

which should be very possible to do

Answer 9

you can calculate each of these chances seperatly and add/multiply them or if you have a calculator that can handle it you can do the whole at once